Optical arrayed waveguide grating devices

ABSTRACT

It is found that the use of a multimode interference (MMI) section to flatten the pass-bands of an arrayed waveguide grating (AWG) multiplexer/demultiplexer or comb filter introduces undesirable non-linear wavelength dispersion into those pass-bands if that MMI section mixes modes of more than two different orders. This dispersion can be substantially compensated by the use of a tandem arrangement of two AWGs with MMIs of differing length chosen to provide complementary dispersions. In the case of a comb filter, an equivalent compensation can be achieved by arranging for the light to make a second passage through the AWG in the reverse direction.

FIELD OF THE INVENTION

This invention relates to optical arrayed waveguide grating (AWG)devices, particularly such devices suitable for use as opticalwavelength multiplexers, demultiplexers, or filters. Such devices findparticular, but not necessarily exclusive, application in wavelengthdivision multiplexed (WDM) optical transmission systems.

BACKGROUND TO THE INVENTION

WDM optical transmission systems ideally require passive opticalwavelength multiplexers, demultiplexers and filters which ideally shouldhave isolated pass-bands which are flat-topped so as to allow a measureof tolerance in the spectral positioning of the individual signals ofthe WDM system within these pass-bands. One method of multiplexing,demultiplexing or filtering channels in an optical WDM system reliesupon the use of multilayer dielectric interference filters. Anotherrelies upon Bragg reflection effects created in optical fibres. A thirdmethod, the method with which the present invention is particularlyconcerned, relies upon diffraction grating effects.

The particular format of optical waveguide diffraction grating withwhich the present invention is concerned is derived from the format thatincludes a set of optical waveguides in side-by-side array, eachextending from one end of the array to the other, and being of uniformlyincrementally greater optical path length from the shortest at one sideof the array to the longest at the other. Such an optical grating,sometimes known as an arrayed waveguide grating (AWG), constitutes acomponent of the multiplexer described by C Dragone et al., ‘IntegratedOptics N×N Multiplexer on Silicon’, IEEE Photonics Technology Letters,Vol. 3, No. 10, October 1991, pages 896-9. Referring to accompanyingFIG. 1, the basic components of a 4×4 version of such a multiplexercomprise an optical waveguide grating array, indicated generally at 10,whose two ends are optically coupled by radiative stars, indicatedschematically at 11 and 12, respectively with input and output sets ofwaveguides 13 and 14. Monochromatic light launched into one of thewaveguides of set 13 spreads out in radiative star 11 to illuminate theinput ends of all the waveguides of the grating 10. At the far end ofthe grating 10 the field components of the emergent light interferecoherently in the far-field to produce a single bright spot at the farside of the radiative star 12. Increasing the wavelength of the lightcauses a slip in the phase relationship of these field components, withthe result that the bright spot traverses the inboard ends of the outputset of waveguides 14 as depicted at 15. If the mode size of thewaveguides 14 is well matched with the size of the bright spot, thenefficient coupling occurs at each of the wavelengths at which the brightspot precisely registers with one of those waveguides 14.

The difference in optical path length between the inboard end of awaveguide 13 and that of a waveguide 14 via adjacent waveguides in thearray 10 (the optical path length of a waveguide being the product ofits physical length with its effective refractive index) determines thevalue of the Free Spectral Range (FSR) of the grating for thisparticular pair of waveguides, being the frequency range over which thisdifference in optical path length produces a phase difference whosevalue ranges over 2π radians. Accordingly the single bright spot isproduced in the same position each time the optical frequency of thelight is changed by an amount corresponding to a frequency differencethat is an integral number of FSRs. It can thus be seen that, foroptical transmission from any particular one of the set of waveguides 13to any particular one of the set of waveguides 14, the device of FIG. 1operates as a comb filter whose teeth are spaced in frequency by the FSRof its grating 10. The propagation distances across the radiative starsthemselves contribute to the FSR of any particular combination ofwaveguide 13 and waveguide 14, and so not all the FSRs are preciselyidentical.

The movement of the bright spot across the end of the particularwaveguide 14 that occurs in consequence of a change of wavelength,results in an approximately Gaussian transmission pass-band for eachchannel of the multiplexer/demultiplexer. For operation in a practicalWDM transmission system a more nearly flat-topped transmission pass-bandis generally a requirement in order to avoid excessive uncertainties inthe value of insertion loss that the device is liable to provide as theresult of tolerances allowed for in the emission wavelengths of theoptical sources employed in that transmission system, and to allow forthe modulation bandwidth of the signals transmitted in the individualWDM channels. In this context, it may be noted that the drive tonarrower channel spacings will typically aggravate this problem because,in general, the tolerances imposed upon the precision of sourcewavelengths are not tightened in proportion to the narrowing of thechannel spacings, and/or the modulation bandwidth tends to constitute agreater proportion of the channel spacing.

In U.S. Pat. No. 5,629,992 there is described a method of providing ameasure of flattening of the transmission pass-band of an AWG thismethod involving the interposing of a length of wider waveguide betweenthe input waveguide 13 and the first star coupler 11. This widerwaveguide (also known as a multimode interference (MMI), or mixer,waveguide section) is capable of guiding, not only the zeroth ordermode, but also the second order mode, both of which are excited by thelaunch of zeroth order mode power into it from the waveguide 13 becausethe transition between the waveguide 13 and its MMI section is abrupt,i.e. is non-adiabatic. These two modes propagate with slightly differentvelocities, and the length of the wider waveguide is chosen to be of avalue which causes π radians of phase slippage between them. Under theseconditions, the field distribution that emerges into the star coupler 11from the end of the wider waveguide is double peaked. The image of thisfield distribution is formed at the end of star coupler 12 that isabutted by the waveguides 14. The overlap integral between this imageand the field distribution of the zeroth order mode of any one of thewaveguides 14 then determines the transmission spectrum afforded by thedevice in respect of the coupling to that waveguide. The amount ofband-pass flattening thereby occasioned can be expressed in terms of anincrease in the value of a Figure of Merit (FoM) parameter arbitrarilydefined as the ratio of the −0.5 dB pass-band width to the −30.0 dBpass-band width. A significant drawback of the mixer section approach topass-band flattening is that the insertion loss is intrinsicallyincreased consequent upon the mismatch between the size of the flattenedfield distribution that is incident upon the inboard end of the outputwaveguide 14 and that of the field distribution of the zeroth order modethat is guided by that waveguide 14. By way of example, a mixer sectionsupporting the zeroth and second order modes can be employed to increasethe FoM of an AWG from about 0.14 to about 0.30, but this improvement inFoM is achieved at the expense of increasing the insertion loss of thedevice by approximately 2 dB. Further flattening can be obtained bywidening still further the width of the mixer section to enable it toguide a larger number of even order modes, but this introduces yethigher increases in insertion loss. For instance, if the FoM isincreased in this way to about 0.45, this is achieved at the expense ofan excess insertion loss of approximately 4 dB. (No explicit mention hasbeen made concerning the propagation of modes of odd order number in theMMI section. This is because generally the MMI section and the inputwaveguide will be arranged symmetrically with respect to each other sothat zeroth order mode power launched into the MMI from the inputwaveguide will not excite modes of odd order number.)

One factor not specifically addressed in the foregoing discussion is thechromatic dispersion afforded by these AWG multiplexer/demultiplexerdevices. The deleterious effects of chromatic dispersion becomes moresignificant as the bit rate of traffic being transmitted in individualchannels is increased.

SUMMARY OF THE INVENTION

An object of the present invention is to provide AWG-basedmultiplexer/demultiplexer and comb filter devices that exhibit not onlyrelatively flat-topped and well isolated pass-bands, but also relativelylow dispersion.

According to a first aspect of the present invention, there is providedan arrayed waveguide grating device having an input/output waveguideoptically coupled with an output/input waveguide via an optical paththat includes, optically in series, first and second arrayed waveguidegratings configured to exhibit matched free spectral ranges to saidoptical path, each of which arrayed waveguide gratings having first andsecond ends respectively terminating in first and second radiative starcouplers associated with that arrayed waveguide grating, which opticalpath additionally includes an intermediate waveguide that opticallycouples the second radiative star coupler of the first arrayed waveguidegrating with the first radiative star coupler of the second arrayedwaveguide, and which optical path also includes first and secondmultimode interference waveguide sections respectively terminating inone of the radiative star couplers of the first arrayed waveguidegrating and in one of the radiative star couplers of the second arrayedwaveguide grating, and wherein the first and second multimodeinterference waveguide sections support at least the zeroth, second andfourth order modes, and their relative lengths are such that, in respectof light launched into their respective waveguides, they produce, wherethey terminate in their respective radiative star couplers, fielddistribution phase fronts possessing substantially complementarycurvatures.

The waveguides of the arrayed waveguide grating devices, and theinput/output, output/input and intermediate waveguides are notnecessarily strictly single mode waveguides, but if, in addition toguiding the zeroth order mode, any of these waveguides does guide one ormore higher order modes, then it is constructed so that those higherorder modes are much more heavily attenuated than the zeroth order modebecause the end-to-end propagation of higher order mode power in such awaveguide is generally found to be detrimental to device operation. Norare these waveguides necessarily of the same cross-section throughouttheir end-to-end length, but may, for instance, incorporate one or moreadiabatic tapers.

According to a second aspect of the present invention, there is providedan arrayed waveguide grating comb filter device having an arrayedwaveguide grating optically coupled via a first radiative star couplerwith first and second waveguides, respectively constituting aninput/output port and an output/input port of the device, and coupledvia a second radiative star coupler with third and fourth waveguides,which comb filter also includes first and second multimode interferencewaveguide sections each of which supports at least the zeroth, secondand fourth order modes and provides an indirect coupling between arespective one of two of said first to fourth waveguides and itsrespective one of said first and second radiative star couplers whileeach of the other two of said first to fourth waveguides is directlycoupled with its respective one of said first and second radiative starcouplers, wherein the third waveguide is optically coupled with thefourth waveguide via an optical isolator, and wherein the relativelengths of the first and second multimode interference waveguidesections are such that, in respect of light launched into theirrespective waveguides, they produce, where they terminate in theirrespective radiative star couplers, field distribution phase frontspossessing substantially complementary curvatures.

Other features and advantages of the invention will be readily apparentfrom, the following description of preferred embodiments of theinvention, from the drawings and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 (to which previous reference has already been made) schematicallydepicts a prior art employing an optical waveguide type diffractiongrating,

FIG. 2 is a schematic diagram of a optical waveguide terminating in amultimode interference (MMI) section,

FIG. 3 is a schematic diagram of an optical multiplexer/demultiplexerdevice constructed in accordance with the teachings of the presentinvention,

FIGS. 4, 5, 6 and 7 are schematic diagrams depicting, on a larger scaleand in greater detail, parts of the device of FIG. 3,

FIGS. 8 and 9 are schematic diagrams of alternative forms of comb filterdevice constructed in accordance with the teachings of the presentinvention,

FIGS. 10 and 11 are schematic diagrams depicting, on a larger scale andin greater detail, parts of the device of FIG. 9,

FIGS. 12, 13 and 14 are schematic diagrams of successive stages in theconstruction of an integrated waveguide optical device in which amultiplexer/demultiplexer embodying the invention in a preferred form isformed, and

FIG. 15 depicts group delay plots of two simulated AWG devicesexhibiting substantially complementary group delay characteristics.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

In FIG. 2 there is schematically depicted an indeterminate length ofoptical waveguide 20 terminating abruptly (non-adiabatically) at 21 in amultimode interference (MMI) section constituted by a section ofmultimode optical waveguide 22 of specific length ‘d’. The fielddistribution of the zeroth order mode of waveguide 20 does not exactlymatch that of the zeroth order mode of multimode waveguide 22 and so,when the zeroth order mode of waveguide 20 is launched into waveguide 22at the junction 21 between these two waveguides, not only is thefundamental (zeroth order) mode of waveguide 22 excited, but also one ormore additional (higher order) modes. Provided that the two waveguidesare coaxial, only even order higher order modes are excited. These modeshave different propagation constants. Accordingly progressive phaseslippage occurs between the zeroth and second order modes as theypropagate away from junction 21. At the distance at which this slippageamounts to π, these two modes combine to produce a field distributionthat, in comparison with the near-Gaussian field distribution of thezeroth order mode on its own, is more nearly flat-topped, even though itis double peaked, exhibiting a slight dip in the centre. If other modesare also present, they will modify still further the field distributionbut, in a conventional design of MMI section for an AWG, the MMI sectionis dimensioned so that the third order mode is only just below cut-offand so that still higher order modes are strongly cut-off. If the MMIsection does not support any mode higher than the second order mode, andif the MMI section were long enough, then the combined fielddistribution would be repeated at each position further along themultimode waveguide 22 at which the phase slippage has been augmented bya further 2π. (If however the MMI section were to support three or moremodes excited by power launched from the waveguide 20, then there wouldnot, in general, be this cyclic pattern because different pairs of modesgenerally have different propagation constant differences, and hencedifferent rates of phase slippage.)

It is generally the case that the shape of the field distribution at thefar end of the MMI waveguide 22 is determined substantially exclusivelyby the interference of the guided modes of that waveguide. Therefore, ifthe multimode waveguide 22 is dimensioned so as not to guide the fourthor any higher order modes, it is only the interference between thezeroth and second order modes that needs to be taken into considerationin the determination of the field distribution at the far end of thatwaveguide.

Reverting attention to FIG. 1, if the set of waveguides 13 were to bereplaced with a single MMI-terminated waveguide as depicted in FIG. 2,whose MMI section dimensioned so that the third order mode is only justbelow cut-off and so that still higher order modes are strongly cut-off,and whose length ‘d’ provides a phase slippage of π between its zerothand second order guided modes, then the resulting double-peaked fielddistribution launched into the first star coupler 11 will be re-imagedat the exit end of the second star coupler 12, the end to which thewaveguides 14 are abutted. A similar imaging will also occur if the MMIsection is modified to be additionally capable of guiding the fourthorder mode and, optionally, even higher even order modes. The differencein propagation constant between the zeroth and second order modes is notgenerally equal to the difference in propagation constant between thesecond and fourth order modes. (More generally, different consecutivepairs of even order modes have different propagation constantdifferences.) Accordingly, the optimum field distribution obtainablefrom the mixing of the zeroth, second and fourth order modes, in termsof the flatness of its top and the steepness of its sides, and optimumthat is better than that obtainable from the mixing of only the zerothand second order modes, occurs for an MMI section length affording aphase slippage between the zeroth and second order modes not exactlyequal to π.

It has been found that a further consequence of the different magnitudesof propagation constant differences is that the phase front of the fielddistribution that is launched into star coupler 11 is no longersubstantially planar, but has a significant curvature. The re-imaging bythe array 10 of the complex field distribution on to the exit end of thesecond star coupler 12, in the presence of this phase front curvature,then gives rise to a non-linear phase response expressed as a functionof wavelength or optical frequency. In other words, the inclusion of theadditional mode, though it enables the further improvement of there-imaged field distribution, it achieves this benefit at the expense ofintroducing a non-linear term into the phase response exhibited by thedevice. This non-linearity is a serious disadvantage in systemsrequiring tight management of dispersion, i.e. group delay that iswavelength dependent across individual passbands of the device. This isbecause it means that there is, in general, an uncertainty in both themagnitude and the sign of the dispersion that the device will afford toa signal propagating through it, this being determined according aswhether this signal is nearer the top end of its signal channel ornearer the bottom end.

In a number of circumstances a concatenation of two AWG devices isrequired to achieve inter-channel cross-talk levels that are low enoughto satisfy a given system specification. It has been found that in suchcircumstances it is possible to provide the two AWGs of theconcatenation with MMIs of different lengths that are inter-related sothat the non-linear dispersion term introduced by the MMI section of thefirst AWG is substantially compensated by that introduced by the MMIsection of the second. In other words, it has been found possible todesign MMI sections to produce field distributions that havesubstantially complementary curvatures.

Attention is now turned to FIG. 3, which schematically depicts amultiplexer/demultiplexer device constructed in accordance with theteachings of the present invention. This device has a single (1×N) AWGmultiplexer/demultiplexer unit 30, to which are connected, in treeconfiguration, a set of N (1×1) AWG filter units 31. (For convenience ofillustration, FIG. 3 depicts a device in which N=4, but it will beappreciated that examples in which N≠4 are equally valid.) All of theunits 30 and 31 have the same general layout of gratings 10 andradiative stars 11 and 12 which are arranged in the same arrangement asin the multiplexer/demultiplexer device of FIG. 1. The gratings 10 aregratings constructed from waveguide. Instead of a set of waveguides 13,as depicted in the multiplexer/demultiplexer device of FIG. 1, the AWGmultiplexer/demultiplexer unit 30 of FIG. 3 has a single MMI-terminatedwaveguide as depicted in FIG. 2, its waveguide being depicted at 32 andits MMI section at 33. To the exit end of the second star coupler 12 ofthe multiplexer/demultiplexer unit 30 is connected a set of waveguides34 corresponding to the set of waveguides 14 of the device of FIG. 1.Similarly, instead of a set of waveguides 13 as depicted in themultiplexer/demultiplexer device of FIG. 1, each AWG filter unit 31 ofFIG. 3 has a single MMI-terminated waveguide as depicted in FIG. 2, itswaveguide being depicted at 35 and its MMI section at 36. The MMIsections 36 of all the units 31 are of identical length, a length whichdiffers from that of the MMI section 33 of the unit 30. Each of the Nwaveguides 34 of unit 30 is optically coupled, by way of one of anassociated set of N waveguides 37, with the waveguide 35 of anassociated one of the set of N units 31 To the exit end of the secondstar coupler 12 of each filter unit 31 is connected a single associatedwaveguide 38.

The AWG unit 30 provides a comb filter function for the passage of lightbetween waveguide 32 and any particular one of the N waveguides 34.Since this unit is performing a wavelength multiplexing/demultiplexingfunction, it is clear that the precise spectral positioning of the combfilter function is different for the passage of light between waveguide32 and each different one of the N waveguides 34. This may bealternatively represented by the statement that the AWG unit 30 provides(slightly) different Free Spectral Ranges (FSRs) between waveguide 32and each one of the N different waveguides 34. In contrast, each of theAWG units 31 has only two external connections, waveguide 36 andwaveguide 38, and so possesses only a single FSR and therefore only asingle comb filter function.

Typically, when the multiplexer/demultiplexer device of FIG. 3 is beingemployed as a multiplexer/demultiplexer, there is only one tooth of eachcomb filter function (only one diffraction order of its grating) that isbeing actively made use of, and so it is only necessary for there to beregistry between this tooth of unit 30 and the corresponding tooth ofthe relevant AWG unit 31. However, such registry may conveniently beachieved by providing the two AWG units with substantially identicalFSRs, thereby providing registry of the entire combs. One way ofachieving this registry is to make each unit 31 identical with unit 30,and then to provide each waveguide 38 with the same offset (with respectto its radiative star coupler 12) as that of the waveguide 34 of unit 30to which that particular unit 31 is connected. A disadvantage of such anapproach is that the provision of an offset introduces additionaloptical loss into the device. It may therefore be preferred not toinclude offsets in the design of the AWG units 31, but instead toachieve the required FSR matches by employing a (slightly) differentvalue of length increment for the array 10 of each of the units 31.

FIG. 4 schematically depicts on a larger scale, and in greater detail,the star coupler 11 of multiplexer/demultiplexer unit 30, together withthe MMI section 33 and adjacent parts of the AWG array 10 and waveguide32. In FIG. 4 the individual waveguides of the AWG array 10 areseparately depicted as waveguides 40. These waveguides terminate at apart of the boundary 41 of the radiative star coupler 11 that preferablyhas the form of an arc of a circle centred in the centre of the oppositeboundary 42 which preferably has the form of an arc of a circle centredin the centre of the first-mentioned boundary 41. The end sections ofthe waveguides 40 are disposed radially so that their axes intersect atthe centre of curvature of the circular arc 41. Optionally, the set ofwaveguides 40 is flanked by two sets of dummy waveguides 43 that arealso disposed radially, but are terminated obliquely after a shortdistance. The function of these dummy waveguides 43 is to place the endsof those of the waveguides 40 that are near the side edges of the arrayin a lateral environment more nearly resembling that of the waveguides40 further away from those side edges. The axis of the end section ofthe waveguide 32 and its MMI section 33 lies on the axis of symmetry ofthe array of radially disposed end sections of waveguides 40.

FIG. 5 schematically depicts on the same scale and detail as employed inFIG. 4, the star coupler 12 of multiplexer/demultiplexer unit 30,together with part of its AWG 10 and part of its array of waveguides 34.The configuration of the star coupler 12 is the same as that of starcoupler 11. Although this FIG. 5 happens to depict the array ofwaveguides 34 as being composed of the same number of waveguides as thenumber of waveguides 40 forming the AWG array, this is not a necessary,or even particularly desirable, relationship. However, the preferredarrangement of the end sections of the waveguides 34 of the array is thesame as that of the waveguides 40 insofar as their arrangement is radialso that their axes intersect at the centre of the further end of thestar coupler 12. Optionally, the array of waveguides 34 may be flankedwith arrays of dummy waveguides 50 that are also disposed radially, butare terminated obliquely after a short distance, these dummy waveguidesserving, if provided, substantially the same function as dummywaveguides 43.

FIGS. 6 and 7 similarly schematically depict on the same scale anddetail as employed in FIGS. 4 and 5, respectively the star couplers 11and 12 of filter unit 31, together with adjacent parts of the waveguides43 of its AWG array 10 and waveguides 35 and 38, additionally depicting,in the case of the star coupler 11 of FIG. 6, the MMI section 36. Thesole difference between the layouts of FIGS. 4 and 6 lies in the lengthsof their respective MMI sections 33 and 36. In the case of the layoutsof FIGS. 5 and 7, the sole difference lies in the substitution, in FIG.7, of the single waveguide 38 for the array of waveguides 34 of FIG. 5,the end section of this waveguide 38 being arranged so that its axislies on the axis of symmetry of the array of radially disposed endsections of waveguides 40.

Reverting attention to the multiplexer/demultiplexer device of FIG. 3,it may be noted that each of its filter units 31 does not have only asingle pass-band, but has a set of pass-bands at a frequency spacingequal to its free spectral range (FSR) which is also the FSR of thedevice. Accordingly, if all that is required is a comb filter function,this can at least in principle be produced by modifying the device ofFIG. 3 by replacing the set of waveguides 34 ofmultiplexer/demultiplexer unit 30 with a single waveguide connected tojust one of the filter units 31, and dispensing with the other (N−1)filter units, thereby producing the structure schematically depicted inFIG. 8.

The two AWGs 10 of the comb filter structure of FIG. 8 are identical,but one of them can be dispensed with by directing the light through theremaining AWG 10 first in one direction, and then in the other, using aconfiguration as schematically depicted in FIG. 9. In this configurationone of the MMI-terminated waveguides, comprising waveguide 32 and MMIsection 33, abuts the end of star coupler 11 in side-by-siderelationship with waveguide 38. Similarly, the other of theMMI-terminated waveguides, comprising waveguide 35 and MMI section 36,abuts the end of star coupler 12 in side-by-side relationship withwaveguide 34. In view of these side-by-side relationships, it is clearthat waveguides 32 and 38 can not both be aligned with the symmetry axisof the radially disposed end sections of the array of waveguides 40 ofAWG 10. Nor either can the axes of waveguides 35 and 34 both be alignedwith this symmetry axis. Accordingly the axes of the end sections ofthese four waveguides are each inclined to this symmetry axis at anangle φ, as schematically depicted in FIGS. 10 and 11, with each ofthese four waveguide axes intersecting the symmetry axis at the remoteend of the star coupler to which that waveguide is abutted.

Under these conditions, the set of pass-bands afforded by the AWG 10 forlight propagating from waveguide 32 to waveguide 34 are matched withthose for light propagating from waveguide 35 to waveguide 38. Waveguide34 is optically coupled with waveguide 35 via an optical path 91 thatincludes an optical isolator 90. The need for this optical isolator 90arises because the AWG 10 also affords a frequency displaced set ofpass-bands to light propagating from waveguide 32 to waveguide 35, andfrom waveguide 34 to waveguide 38.

If the optical path 91 is constructed in polarisation state preservingwaveguide, there can be advantage in connecting its ends so that thepolarisation state with which light emerges from the AWG 10 intowaveguide 34 is orthogonal to the polarisation state with which thatlight is launched back into the AWG 10 from waveguide 35. This isbecause any polarisation dependent effects consequent upon the lightmaking its first transit through the AWG 10 are substantiallycompensated when it makes its second transit.

In the foregoing description with particular reference to FIGS. 3 and 4the AWG unit 30 has been described as having its MMI section 33terminated waveguide 32 at radiative star coupler 11 but, inasmuch asthis AWG unit is a reciprocal device, it will be evident that the placeof the MMI section 33 on waveguide 32 could alternatively be taken by aset of N such MMI sections, one terminating each one of the waveguides34 at radiative star coupler 12. By the same reasoning, it is clear thatthe place of MMI section 36 of any or all of the AWG units 31 can beswitched from waveguide 35 to waveguide 38. Similarly, in the case ofthe AWG unit of FIG. 9, it can be seen that the two MMI sections 33 and36 can be located on any pair of the four waveguides 32, 34, 36 and 38.Thus, for instance, if the MMI units 33 and 36 respectively terminatewaveguides 32 and 34, then the filter's input is provided by way ofwaveguide 38, the relevant matching FSRs are those between waveguides 38and 34 and between waveguides 36 and 32, and the filter's output isprovided by way of waveguide 32.

Earlier, reference has been made to the fact that waveguides mayincorporate adiabatic tapers, but even where any of the waveguides 32,34, 35, 38 and 40 have, in physical reality, incorporated such tapers,these tapers have not, for convenience of illustration, beenspecifically illustrated in any of the FIGS. 4 to 7, 10 and 11.

The method of constructing the AWGs 10 of FIGS. 3 to 11 uses a knownform of processing to create the required configuration of opticalwaveguides in an integrated waveguide optics structure. Successivestages of this processing are schematically illustrated in FIGS. 12, 13and 14. Referring in the first instance to FIG. 12, a layer 121 ofcladding glass, typically a layer of silica, is deposited upon a planarsubstrate 120, typically a silicon substrate. On layer 121 is depositeda layer 122 of core glass having a refractive index a controlled amountgreater than that of the cladding glass layer upon which it isdeposited. Typically the core glass layer 122 is composed of dopedsilica. Standard photolithographic techniques are then used to patternthis layer to define the required configuration of waveguides. Theportion of integrated waveguide optics structure illustrated in FIGS.12, 13 and 14 includes portions of a number of optical waveguides 123 ineach of which a waveguiding effect is provided both in the directionnormal to the plane of the layer 122 and in the direction lying in theplane of that layer that is at right-angles to the axial direction ofthat waveguide. For convenience of illustration, only four of thosewaveguides 123 have been specifically illustrated in FIGS. 13 and 14,though it is to be understood that in practice a grating may typicallyactually have between 20 and 30 of such waveguides. These fourwaveguides 123 are shown terminating in a planar waveguide region 124,part of one of the star couplers 11 or 12 in which there is still awaveguiding effect in the direction normal to the plane of layer 122,but in which light is able to radiate laterally from any one of thewaveguides 123. After completion of the patterning of layer 122, it iscovered with a further layer 125 of cladding glass whose refractiveindex is less than that of core glass layer 122, preferably having anindex matched with that of cladding glass layer 121. Typically thiscladding glass layer 125 is also made of doped silica, the doping inthis instance not being chosen to raise the refractive index of the hostmaterial, but to lower its flow temperature.

Attention is now turned to how the respective lengths of the two MMIsections 33 and 36 may be selected to achieve the required fielddistributions with substantially complementary curvatures.

For this purpose, the propagation of light through the AWG device ismodelled as a function of optical frequency for a range of deviceparameter values using the Effective Index Method (EIM) described forinstance at pages 90-91 of the book by J Carroll et al. entitled,‘Distributed feedback semiconductor lasers’ published in 1998 by TheInstitute of Electrical Engineers (ISBN 0 85296 917 1). The EIM approachprovides an effective one-dimensional waveguide refractive index profilewhose propagation characteristics model those of an actualtwo-dimensional waveguide refractive index profile. The EIM isparticularly suited for analysing light propagation in an AWG devicebecause in such a device the refractive index profile of its waveguidesin the direction normal to the plane of the substrate surface upon whichthe waveguides are supported is the same throughout the device. Thechosen orientation of the one-dimension of the effective one-dimensionalwaveguide refractive index profile is the direction that is contained inthe plane of the substrate surface upon which the waveguides aresupported, and is at right-angles to the axis of that waveguide (i.e. itdescribes a lateral profile). Once the refractive index and dimensionalparameters of the two-dimensional waveguide that constitutes the inputwaveguide of the AWG device have been employed to determine theequivalent parameters of its effective one-dimensional waveguidecounterpart, the modelling continues with the calculation of the(lateral) electric field distribution of the guided zeroth order mode inthis effective one-dimensional waveguide.

If there is an MMI section between the input waveguide and the firstradiative star coupler of the AWG device, then the excitation of thevarious guided modes in the MMI section are calculated from the overlapintegral of each of its guided modes with the input excitation field.The output from the MMI section is calculated from the summation of thefield distribution of each of these guided modes, with an appropriatephase shift corresponding to the propagation along the MMI section. Ifthere is no MMI section, then the field profile of the zeroth order modein the input guide is launched straight into the first radiative starcoupler. The complex field distribution on the far side of the firststar coupler is calculated allowing for free diffraction across thisstar coupler.

The effective one-dimensional waveguide counterparts of thetwo-dimensional waveguides that constitute the waveguides of the gratingarray are calculated using the EIM in the same way as for the inputwaveguide. As before, overlap integrals are used to calculate theexcitation of the guided modes. In this case the field pattern that haspropagated across the star coupler, and that of the zeroth order mode atthe input end of each array waveguide, are used to calculate thestrength of the excitation of the mode guided in that array waveguide.The propagation through each array waveguide is often assumed to beindependent of every other array waveguide. In practice there will be atleast some lateral coupling between adjacent waveguides of the array,especially near their ends where they are more closely spaced thanelsewhere, but it is often found that the effect of this coupling issmall enough for it to be unnecessary to take account of it in thecalculation. The complex field at the output of each array waveguide,where it abuts the second radiative star coupler, is calculated from theinput field, allowing for the appropriate phase shift associated withthe propagation along the specific length of that array waveguide. Ifthere is significant differential attenuation between the differentwaveguides of the array, this will also need to be taken into account inthe calculation.

The effective one-dimensional waveguide counterpart of the or eachoutput waveguide whose input end abuts the second radiative star coupleris calculated using the EIM in the same way as for the input waveguide.The complex field profile in the plane of the or each output waveguideat the output of the second star coupler is calculated by allowing forthe free diffraction from each array waveguide across the star coupler.Finally the strength of the zeroth order mode excitation in the outputwaveguide, and its phase, are estimated from the overlap integral of thecomplex field profile at the output of the second star coupler with thezeroth order mode at the input of the or each output waveguide. Thecalculation thus provides an electric field vector in the complex formE_(r)+jE_(j), which describes the amplitude and phase of the lightoutput from the AWG device in relation to the light input to the devicewith an electric vector E. The amplitude and phase (φ) response of theAWG device as a function of optical frequency can then be built up byiterating the calculation process for a family of spectrally adjacentoptical frequencies. Then, it is possible to evaluate the group delay,τ_(g), where τ_(g)=dφ/dω, and ω=2πf and f is the optical frequency.

In the case of an AWG device with a single MMI section in its singleinput waveguide, two design variables are immediately apparent, thewidth of the MMI section, and its length. In fact there are two furtherdesign variables, namely the width of the input waveguide where it abutsthe MMI section, and the width of the or each output waveguide where itabuts the second radiative star coupler. These latter two widths are notnecessarily preserved for the full lengths of their respective input andoutput waveguides, but may be linked by adiabatic tapers with regions ofdifferent width.

These calculations enable an assessment of the performance of the AWGdevice design to be made in terms of the additional attenuationresulting from the use of the MMI section, the Figure of Merit (FoM) ofthe spectral profile of the device (conveniently expressed in terms ofthe −0.5 dB and −30.0 dB spectral widths), and the ripple in itspassband (conveniently expressed in terms of the difference in dBsbetween the highest peak of the pass-band and its lowest trough).Following on from this, it is possible to repeat the calculations fordifferent values of the four variables, for instance exploring theeffect of varying the magnitude of each variable in turn while theothers are maintained constant, in order to build up a map of how thefour variables tend to affect performance, and thereby enable theselection of optimised values.

The ensuing table sets out the calculation results in respect of an AWGdevice designed to have a free spectral range (FSR) approximately equalto 100 GHz, a channel spacing of half this value and a centre (freespace) wavelength of 1545 nm. The refractive index of its opticalcladding is 1.4464, while that of its waveguide cores is 1.4574. Thewaveguide cores are 7 μm thick and, except where specially widened, are5.5 μm wide. The grating array consists of 15 array waveguides that areon a pitch of 25 μm where their ends abut the first and second radiativestar couplers of the device. At these ends, the width of each arraywaveguide is 21.5 μm. The set of output waveguides are on a pitch of 35μm where their ends abut the second radiative star coupler. In theensuing table, W_(i) is the width of the input waveguide where it abutsthe MMI section; W_(s) is the width of the MMI section, while L_(s), isits length; W_(o), is the width of the output waveguide where it abutsthe second radiative star coupler; A (dB) is the additional attenuationof the device, FoM is its Figure of Merit, and R (dB) is the ripple.

W_(i) W_(s) W_(o) L_(s) A (dB) FoM R (dB) 10 30 12 370 4.37 0.14 0.68 1130 12 370 4.22 0.17 0.54   11.5 30 12 370 4.14 0.47 0.48 12 30 12 3704.07 0.45 0.42 13 30 12 370 3.92 0.43 0.3  14 30 12 370 3.76 0.41 0.1916 30 12 370 3.45 0.37 0   14 30 12 360 3.59 0.34 0   14 30 12 365 3.680.38 0.31 14 30 12 370 3.76 0.41 0.19 14 30 12 375 3.85 0.43 0.15 14 3012 380 3.94 0.45 0.17 14 30 12 390 4.12 0.47 0.34 14 30 12 400 4.31 0.490.62 14 30 12 410 4.5  0.51 0.91 14 27 12 370 3.97 0.48 0.92 14 28 12370 4.01 0.48 0.71 14   28.5 12 370 3.98 0.47 0.53 14 29 12 370 3.920.45 0.25 14 30 12 370 3.76 0.41 0.19 14   30.5 12 370 3.67 0.35 0   1431 12 370 3.58 0.17 0   14 32 12 370 3.41 0.14 0   14 30  9 370 4.360.46 0.3  14 30 10 370 4.17 0.45 0.27 14 30 11 370 3.96 0.43 0.25 14 3012 370 3.76 0.41 0.19 14 30 13 370 3.57 0.39 0.21 14 30 14 370 3.38 0.370  

From the foregoing table was selected the design that has an inputwaveguide width, W_(i) , of 14 μm, an output waveguide width, W_(o), of12 μm, an MMI section width, W_(s), of 30 μm and length, L_(s), of 380μm. Trace 151 of FIG. 15 depicts the calculated group delay exhibited bythis AWG device, calculated on the basis that the individual arraywaveguides are subject to statistically distributed optical path lengtherrors of a magnitude not exceeding 75 nm. The group delay is thus seento vary, within the pass-band, in a highly non-linear way with a rangeof more than 15 ps. The MMI section length of 380 μm is not equal to thelength, 517 μm, for which such an MMI section affords a phase slippageof π between the zeroth and second order modes, being less than thisvalue by 137 μm. Trace 152 of FIG. 15 depicts the calculated group delayexhibited by a second AWG device only in respect of the length of itsMMI section, this length being 654 μm. It is thus seen thatcomplementary group delay characteristics, and hence substantiallycomplementary phase curvatures, are provided by pairs of matching AWGdevices that differ only in respect of the length of their respectiveMMI sections, one being such that the phase slippage between zeroth andsecond order modes is (π−ψ), while that of the other is (π+ψ).

What is claimed is:
 1. An arrayed waveguide grating device having aninput/output waveguide optically coupled with an output/input waveguidevia an optical path that includes, optically in series, first and secondarrayed waveguide gratings configured to exhibit matched free spectralranges to said optical path, each of which arrayed waveguide gratingshaving first and second ends respectively terminating in first andsecond radiative star couplers associated with that arrayed waveguidegrating, which optical path additionally includes an intermediatewaveguide that optically couples the second radiative star coupler ofthe first arrayed waveguide grating with the first radiative starcoupler of the second arrayed waveguide, and which optical path alsoincludes first and second multimode interference waveguide sectionsrespectively terminating in one of the radiative star couplers of thefirst arrayed waveguide grating and in one of the radiative starcouplers of the second arrayed waveguide grating, and wherein the firstand second multimode interference waveguide sections support at leastthe zeroth, second and fourth order modes, and their relative lengthsare such that, in respect of light launched into their respectivewaveguides, they produce, where they terminate in their respectiveradiative star couplers, field distribution phase fronts possessingsubstantially complementary curvatures.
 2. A device as claimed in claim1, wherein said input/output and output/input waveguides of the deviceare the sole input/output and output/input waveguides of the device. 3.An arrayed waveguide grating comb filter device having an arrayedwaveguide grating optically coupled via a first radiative star couplerwith first and second waveguides, respectively constituting aninput/output port and an output/input port of the device, and coupledvia a second radiative star coupler with third and fourth waveguides,which comb filter also includes first and second multimode interferencewaveguide sections each of which supports at least the zeroth, secondand fourth order modes and provides an indirect coupling between arespective one of two of said first to fourth waveguides and itsrespective one of said first and second radiative star couplers whileeach of the other two of said first to fourth waveguides is directlycoupled with its respective one of said first and second radiative starcouplers, wherein the third waveguide is optically coupled with thefourth waveguide via an optical isolator, and wherein the relativelengths of the first and second multimode interference waveguidesections are such that, in respect of light launched into theirrespective waveguides, they produce, where they terminate in theirrespective radiative star couplers, field distribution phase frontspossessing substantially complementary curvatures.
 4. A device asclaimed in claim 3, wherein the third and fourth waveguides are coupledvia the isolator such that light of any polarisation state launched intothe third waveguide from the second radiative star coupler is launchedfrom the fourth waveguide back into the second radiative star coupler inthe orthogonal polarisation state.